In his successful partnership with director Barry Levinson, Johnson produced all of Levinson's films (through 1994) including Rain Man, which won four Academy Awards including Best Picture as well as a Golden Globe for Best Picture, Good Morning Vietnam, The Natural and their 1982 debut project Diner.

Other films made during this period include Avalon, Bugsy, which was nominated for ten Academy Awards including Best Picture and won the Golden Globe for Best Picture, Tin Men and Young Sherlock Holmes.

In 1994, Johnson established his own production company. He produced the critically acclaimed and Los Angeles Film Critics New Generation Award-winner A Little Princess, and the quirky comedy Home Fries, starring Drew Barrymore. Johnson also produced the dramatic thriller Donnie Brasco, starring Al Pacino and Johnny Depp. He is currently the executive producer of the CBS hit drama The Guardian. He has either presented or executive produced Sniper, Bob Roberts, Kafka, Quiz Show and Journey of Hope

Johnson is currently producing the screen adaptation of C.S. Lewis' The Lion, The Witch and the Wardrobe.

Johnson serves as the chairman of the Academy of Motion Picture Arts and Sciences' foreign language film award selection committee.